English

Abstract evolution equations with an operator function in the second term

Functional Analysis 2022-12-21 v2

Abstract

In this paper, having introduced a convergence of a series on the root vectors in the Abel-Lidskii sense, we present a valuable application to the evolution equations. The main issue of the paper is an approach allowing us to principally broaden conditions imposed upon the right-hand side of the evolution equation in the abstract Hilbert space. In this way, we come to the definition of the function of an unbounded non-selfadjoint operator. Meanwhile, considering the main issue we involve an additional concept that is a generalization of the spectral theorem for a non-selfadjoint operator.

Keywords

Cite

@article{arxiv.2207.04392,
  title  = {Abstract evolution equations with an operator function in the second term},
  author = {Maksim V. Kukushkin},
  journal= {arXiv preprint arXiv:2207.04392},
  year   = {2022}
}

Comments

arXiv admin note: text overlap with arXiv:2112.10396

R2 v1 2026-06-25T00:47:19.268Z